Mapytex/mapytex/calculus/polynom.py

#!/usr/bin/env python
# encoding: utf-8


from .expression import Expression
from .operator import op
from .random_expression import RdExpression
from .abstract_polynom import AbstractPolynom

from functools import wraps
import inspect

__all__ = ["Polynom"]


def polynom_factory(func):
    """
    Decorator which specify the type of polynom that the function returns
    """
    @wraps(func)
    def wrapper(*args, **kwrds):
        P = func(*args, **kwrds)
        if issubclass(type(P), AbstractPolynom) and P.degree == 2:
            from .polynomDeg2 import Polynom_deg2
            new_P = Polynom_deg2(poly=P)
            new_P.steps = P.steps
            return new_P
        elif issubclass(type(P), AbstractPolynom):
            new_P = Polynom(poly=P)
            new_P.steps = P.steps
            return new_P
        else:
            return P
    return wrapper


class Polynom(AbstractPolynom):

    """Polynom view as a function.

    It can be initiate like a AbstractPolynom
    # Put example
    Randomly
    # Put example
    It can be evaluate
    # Put example
    And derivate
    # Put example

    """

    @classmethod
    def random(
            self,
            coefs_form=[],
            conditions=[],
            letter="x",
            degree=0,
            name="P"):
        """ Create a random polynom from coefs_form and conditions

        :param coefs_form: list of forms (one by coef) (ascending degree sorted)
        :param conditions: condition on variables
        :param letter: the letter for the polynom
        :param degree: degree of the polynom (can't be used with coefs_form, it will be overwrite) - can't be higher than 26 (number of letters in alphabet)

        /!\ variables need to be in brackets {}

        >>> Polynom.random(["{b}", "{a}"]) # doctest:+ELLIPSIS
        < Polynom x ...
        >>> Polynom.random(degree = 2) # doctest:+ELLIPSIS
        < Polynom_deg2 x ...>
        >>> Polynom.random(degree = 3) # doctest:+ELLIPSIS
        < Polynom x ...>
        >>> Polynom.random(degree = 2, conditions=["{b**2-4*a*c}>0"]) # Polynom deg 2 with positive Delta (ax^2 + bx + c)
        < Polynom_deg2 x ...>
        >>> Polynom.random(["{c}", "{b}", "{a}"], conditions=["{b**2-4*a*c}>0"]) # Same as above
        < Polynom_deg2 x ...>

        """
        if (degree > 0 and degree < 26):
            # Générer assez de lettre pour les coefs
            coefs_name = map(chr, range(97, 98 + degree))
            coefs_form = ["{" + i + "}" for i in coefs_name][::-1]

        form = str(coefs_form)
        # On créé les valeurs toutes concaténées dans un string
        coefs = RdExpression(form, conditions)()
        # On "parse" ce string pour créer les coefs
        coefs = [eval(i) if isinstance(i, str) else i for i in eval(coefs)]
        # Création du polynom
        return Polynom(coefs=coefs, letter=letter, name=name)

    def __init__(self, coefs=[1], letter="x", name="P", poly=0):
        """Initiate the polynom

        :param coef: coefficients of the polynom (ascending degree sorted)
            3 possibles type of coefficent:
                - a : simple "number". [1,2] designate 1 + 2x
                - [a,b,c]: list of coeficient for same degree. [1,[2,3],4] designate 1 + 2x + 3x + 4x^2
                - a: a Expression. [1, Expression("2+3"), 4] designate 1 + (2+3)x + 4x^2
        :param letter: the string describing the unknown
        :param name: Name of the polynom

        >>> P = Polynom([1, 2, 3])
        >>> P.mainOp
        +
        >>> P.name
        'P'
        >>> P._letter
        'x'
        >>> Polynom([1]).mainOp
        *
        >>> Polynom([0, 0, 3]).mainOp
        *
        >>> Polynom([1, 2, 3])._letter
        'x'
        >>> Polynom([1, 2, 3], "y")._letter
        'y'
        >>> Polynom([1, 2, 3], name = "Q").name
        'Q'
        """
        if poly:
            coefs = poly._coef
            letter = poly._letter
            name = poly.name

        super(Polynom, self).__init__(coefs, letter, name)

    def __call__(self, value):
        """ Evaluate the polynom in value

        :returns: Expression ready to be simplify

        >>> P = Polynom([1, 2, 3])
        >>> P(2)
        17
        >>> for i in P(2).explain():
        ...     print(i)
        3 \\times 2^{  2 } + 2 \\times 2 + 1
        3 \\times 4 + 4 + 1
        12 + 4 + 1
        16 + 1
        17
        >>> Q = P("1+h")
        >>> print(Q)
        3 h^{  2 } + 8 h + 6
        >>> R = P(Q)
        """
        eval_exp = self.replace_letter(value)

        return eval_exp.simplify()

    def derivate(self):
        """ Return the derivated polynom

        >>> P = Polynom([1, 2, 3])
        >>> Q = P.derivate()
        >>> Q
        < Polynom x [2, 6]>
        >>> print(Q.name)
        P'
        >>> for i in Q.explain():
        ...     print(i)
        2 \\times 3 x + 1 \\times 2
        6 x + 2
        """
        derv_coefs = []
        for (i, c) in enumerate(self._coef):
            derv_coefs += [Expression([i, c, op.mul])]

        ans = Polynom(derv_coefs[1:]).simplify()
        ans.name = self.name + "'"
        return ans

# Decorate methods which may return Polynoms
methods_list = ["__add__", "__call__", "__mul__", "__neg__", "__pow__",
                "__radd__", "__rmul__", "__rsub__", "__sub__", "derivate",
                "reduce", "simplify", "random"]
for name, func in inspect.getmembers(Polynom):
    if name in methods_list:
        setattr(Polynom, name, polynom_factory(func))


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